Commenting, Cllr Jerry Roodhouse (Paddox), said:
"When the results had come in I had a text from Seb Lowe [Conservative leader of Rugby council] to say, 'you are now the official opposition'.
"It's been a very difficult election, we've had three elections in one go and because of covid we haven't been able to be out in the community meeting with people as much as we would normally be doing.
"But we've held our seats against a wave of blue across the country - it's been heartening for us that people still recognise the work we've been doing in the community.
"As the new opposition we are going to be pushing for our priorities - we will be giving constructive criticism to the Conservatives where needed but we will work with them when it is appropriate.
"One of our priorities is looking at forming a Rugby town council. If Rugby council is abolished, or if it is merged with Nuneaton or Bedworth council, we will need our town centre to be represented.
"The urban area in the town is not part of a parish - so we will need to form a council to make sure it's represented.
"We also want to look at setting up rural traveller sites. When there are no sites for travellers to go to they will set up in inappropriate areas - like they have done recently at St Andrew's Rugby Club.
"This costs the taxpayer a huge amount of money to deal with.
"I've been around for a long time and worked in different councils, in Sussex we made arrangements with the police so that travellers could be evicted within 24 hours - we need to look at doing that here."
"The climate emergency is a major priority, we need to put our foot on the accelerator because not enough is being done by the current portfolio holder.
"Their working group has been given hundreds of thousands of pounds to bring in consultants and work towards a solution - but things are not moving fast enough.
"Overall we want to create a fairer, kinder council, and we will push for better housing, mental health care and care for the elderly."